Nursery school and pre-school are both interchangeable to describe the first part, but not kindergarten, and not nursery without the word school. 

(A nursery is either in a hospital where the newborns are. We also used it in my church to say where the youngest kids went who were not old enough for Sunday School. And in most states, kindergarten is part of the elementary/primary school and is funded through public funds, and is required. Children generally have to be five years old to start kindergarten, so some kids with birthdays late in the year, after the school year starts, go to pre-school for three years.)

In America, the other place is generally called a day care center. This term is very expansive: "Where does your son go to day care?" "He's with my mom two days a week and a neighbor the rest of the week." or "He goes to Tiny Tots, the day care place next door to where I work."

A crèche is a place where mothers (or sometimes father) can leave their very young children while the parent is at work or at a meeting, church service or other activity.

Many children go to nursery school (the word 'school' is generally used by people I know) at the age of three.

Compulsory primary education begins at the age of five, though many primary schools now have 'pre-school' or nursery school departments.


The terms 'play school' and 'kindergarten/kindergarden' used to be alternatives to 'nursery school', but they appear to have gone out of fashion in recent years.